6. What is value of y that is no y = sin-1 x? A. 0 С. B.

Q: Determine the value of f(z) = e*cos y+ ie*sin y at z = In 4+ Ti/6

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Q: a L{sin at} = s2 + a?

A: We have, Therefore,

Q: If y = cos? x – sin? x, what is y? X - х, | dx

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Q: 1 |+tan¬(x), then x2 dy If y=cot-= dx

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Q: d [sin? (In x)] dx

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Q: (p² –1)cos[cosh (In r)]dr

A: In this question, we need to find the integral.

Q: 2ーてスース+スニ。 A ind yh ans: スi:z )スてニリ人3:)

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Q: Calculate the length of the side XY given the following data for 29°: Sin 29° = 0.485 Cos 29° =…

A: Solve for xy

Q: 4/ Solve The DE: [x+y Cot()ay-yx=si

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Q: Show that coshr + sinh r = e" and cosh r - sinhr = e. Hence, deduce M MOUTMOUT cosh? a – sinh? r 1.…

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Q: Compute the indicated quantity using the following data. 12 sin a = 13 where = < a < T 2 cos B 3…

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Q: If y = sin?t+ tant, x= - In(- cost)-e sinr, find the value of y whent=: 4 3/2 (B 2- Vze ? 6. (C) 2+…

A: Given y=sin2t+tant and x=-ln(-cost)-esint

Q: a. Y = cot(Ve“ ) tanh(e") -1 (sin(x²)) tan(2²) tan(ray) = x + y? b. y = C.

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Q: e Suppose flx) = Sin (x) For which value %3D of a, osas T, will f'la) = 0.

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Q: If sin(x +y) = xy, what is the correct expression for -? dx cos(x + y) – y (A х-1 cos(x + y) – y (B…

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Q: Using Simpson's rule, the approximation value for the o sin(x)dæ is : Select one: a. 1.024 b. 0.425…

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Q: For y = sin? x+cos x, y' =

A: Given that, y=sin2x+cos2x We have to find derivative of the given function. Here, y'=dydx

Q: If lF· dĩ = L, where C : x = 2 cos t, y = 3 sin t, t E [0, 7], type in the value of fe F · dī where…

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Q: b) Describe, the motion of a particle with position (x,y) as t varies in' tthe given interval X= 5+…

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Q: 2. If P(x, y) is on the unit circle, then x? + y? = So for all i we have sin't + cost =

A: We Know that, In case of the unit circle: Radius r = 1 and  Standard form of circle passes through…

Q: B) If sinh e V3 Find cosh 0, tanh 0, coth 0.

A: The function sinh(θ) is called the hyperbolic sine function. It is defined as sinh(θ)=eθ-e-θ2.…

Q: Which of the following is correct? 1. cosh?x +sinh²x = 1. II. sinh x cosh y = sinh (x + y) + sinh (x…

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Q: S sin*xcos?x dx

A: The given integral is ∫sin4xcos2xdx. use the identities:sinxcosx=sin2x2sin2x=1-cos2x2 The integral…

Q: Н.W 是, and , if ay Find ax Je az 11. f(x. y) = sin(y- x) 12. f(x. y) = tan %3D %3D por

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Q: If u = tan- the value of x2 +y? +xy du du at x = 1 and y = 3 is

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Q: Eliminate the parameter t from the following. Sa(t) = 2 sin t + 5 ly(t) = 5 cost – 6

A: Rewriting the given equations:

Q: 9. Decide whether or not the following equations are true or false: e° = cos" r + sin² r = cosh? r –…

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Q: dy - y = x? sin(x) dx

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Q: 3. What we want to do next is write (x + jy)as Reie where R= J(x? + y? ) and tan-(e) = (2)

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Q: If y = sin?t+ tant, x=- In(- cost) – e sinr, find the value of y' when 3/7 -VEle 6/2 2-Vze ? 2/3…

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Q: that y?=x+ sin Cxy) - T 2 and let ß Be the value of dy evalwated atlxy

A: Given- y2=x2+sinxy-π24 To Find- The value of dydx at π2,1 and considering that value as β and then…

Q: How many petals does the rose curve r = 3 sin 40 have in the interval [0, T]? O 16 O 4 O 8

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Q: FIND dy/dx for the following Question sin x.cos x 3 y cot x 4. tan x 27) (ans.: )) x(1+ 2 In x) 1+…

A: The given functy43=sinx.cosx1+2.lnx    ....1to find dydx

Q: Find S z? sin z dz

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Q: 6 3 oy sin (a? + 3²) dædy Find

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Q: 4 pts Two angles, X and Y , are complementary. If cos(X)=, what is sin(Y) ? O not enough information…

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Q: 1. y = sin x at , 1)

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Q: FIND dy/dx for the following Question sin x.cos x 1+2.In x 3 y cot x (ans.: 4 tan x 2 27) 2 x(1+ 2…

A: Given: y43=sinx cosx1+2ln x   ...(1)To find : dydx=?Formula: sin 2x=2sin x cos xcos 2x =cos2 x-sin2…

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Q: How many points lie on the intersection of the horizontal line y = c and the graph of y = sin x for…

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Q: Which of the following is correct? 1. cosh²x + sinh²x = 1. II. sinh x cosh y = sinh (x + y) + sinh…

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Q: Find the value of dw / ds at s = 0 if w = sin (e√r) and r = 3sin (s + π/6).

A: w=siner,  r=3sins+π6 Differentiating w=siner with respect to r, we get…

Q: S sin* e de 4

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Q: Given: z = cos(xy) dz Find: ду dz ду dz - tan(xy) = -x sin(xy) ду dz = tan(xy) = -y sin(xy) ||

A: Given: z=cos (xy)Find: ∂z∂y=?

Q: How many points lie on the intersection of the horizontal line y = c and the graph of y = sin x for…

A: The equations are: y = c y = sin x where 0 &lt; x &lt; 2π

Q: y 2+ TT 3 2 -2+ -37

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Q: 4. The teardrop x = 2a cos t – a sin 2t, y = b sin t, 0 < t < 27 find area y 2a

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Q: r=4costheta. Interval pi/4 lessthan/equal to theta less than or equal to 3pi/4

A: We need to draw the polar curve in the given interval.

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.